1. Points, Lines and Planes
Objectives
Identify, name, and draw points, lines, segments, rays, and planes.
Apply basic facts about points, lines, and planes.

2. Points, Lines and Planes
Vocabulary
undefined term point
line plane
collinear coplanar
segment endpoint
ray opposite rays
postulate

3. Points, Lines and Planes
The most basic figures in geometry are undefined terms, which cannot be defined by using other figures.
Point These are the
Line building blocks
Plane of geometry

4. Points, Lines and Planes
Vocabulary
A Point is simply a location

5. Points, Lines and Planes
Vocabulary
A Line is made up of points and has no thickness or width. Points on the same line are said to be collinear. D C B A
These points are collinear

6. Points, Lines and Planes
Vocabulary
A Plane is a flat surface made up of points. Points that lie on the same plane are said to be coplanar. A plane has no depth and extends infinitely in all directions.

7. Points, Lines and Planes

8. Example 1 – Name Lines and Planes
A line containing point N
The line can be named as line c.
There are three points on the line. Any two of the
points can be used to name the line. c A O N M P

9. Example 2 – Name Lines and Planes
A plane containing points P and M
The plane can be named as plane A.
You can also use the letters of any three noncollinear points to name the plane.
Examples: plane MNP plane MOP plane NOP.
There are 18 different 3-letter names for this plane. c A O N M P

10. Example 3 – Draw Geometric Figures
ALGEBRA Lines AB and CD intersect at E for A(-4, 3), B(2, -1), C(2, 4) and D(-4, -2) on a coordinate plane. Point G is coplanar with these points, but not collinear with or 5 C A 4 3 2 G 1 -6 -4 -2 2 B 4 6 D -1 -2 -3 -4 -5

11. Example 4 – Draw Geometric Figures
lies in plane P and contains point Y P X Y W

12. Example 5 – Draw Geometric Figures
a. How many planes appear in this figure? Y R Q T P X Z

13. Example 5 – Draw Geometric Figures
b. Name three points that are collinear. Y R Q T P X Z

14. Example 5 – Draw Geometric Figures
c. Are points X, Y, Z, and P coplanar? Explain. Y R Q T P X Z

15. Example 6 – Draw Geometric Figures
d. At what point do lines PR and TZ intersect? Y R Q T P X Z

17. Understanding Points, Lines and Planes
Example 7 – Draw Geometric Figures
Draw and label each of the following.
A. a segment with endpoints M and N.
B. opposite rays with a common endpoint T.

18. Understanding Points, Lines and Planes
Example 8 – Draw Geometric Figures
Draw and label a ray with endpoint M that contains N.

19. Understanding Points, Lines and Planes
A postulate, or axiom, is a statement that is accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties.

20. Understanding Points, Lines and Planes

21. Understanding Points, Lines and Planes
Example 9
Name a line that passes through two points.

22. Understanding Points, Lines and Planes
Example 10
Name a plane that contains three noncollinear points.

23. Understanding Points, Lines and Planes

24. Understanding Points, Lines and Planes
Example 11 - Representing Intersections
A. Sketch two lines intersecting in exactly one point.
B. Sketch a figure that shows a line that lies in a plane.

25. Understanding Points, Lines and Planes
Example 12 - Representing Intersections
Sketch a figure that shows two lines intersect in one point in a plane, but only one of the lines lies in the plane.

26. Understanding Points, Lines and Planes
Example 13
1. Two opposite rays.
2. A point on BC.
3. The intersection of plane N and plane T.
4. A plane containing E, D, and B.

27. Understanding Points, Lines and Planes
Example 14
Draw each of the following.
A line intersecting a plane at one point
A ray with endpoint P that passes through Q